LMS HMESHER Automatic Mesh Generation for Complex CAD Assemblies

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LMS HMESHER - Automatic Mesh Generation for
Complex CAD Assemblies

• Iulian Grindeanu, LMS International
• Hideaki Ozaki, Honda RD Co., Ltd., Automobile
  RD Center

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Outline

• HMesher history
• Integration in Virtual Lab
• HMesher basic flow
• Zonal meshing
• Examples

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HMesher Development

• Started from PolyFEM mesher. PolyFEM is a p-type
  finite element tool
• Some attributes of PolyFEM mesher
• Start from CAD geometry
• Conforming meshes in CAD assemblies
• Relatively coarse mesh, associated with geometric
  boundary
• Agglomeration of tetras into hexas and pentas.
• QT connections are allowed by PolyFEM solver
• HMesher as opposite to p-mesher (for an h-type
  FE)
• Designed for NASTRAN
• Sought properties hexa meshing
• Coarse mesh
• Conformity to geometry

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HMesher Integration

• Part of LMS Virtual.Lab
• LMS Virtual.Lab is a software suite used to
  simulate the performance of mechanical systems in
  terms of structural integrity, noise and
  vibration, durability, system dynamics, ride and
  handling
• LMS Virtual.Lab is based on CAA V5, the open
  middleware for PLM from Dassault Systèmes.
• There are other meshers available in Catia V5
• Octtree mesher, INRIA mesher
• The actual meshing process is done outside CATIA,
  but geometry extraction and importing of the mesh
  are done using API tools, CAA interfaces.

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HMesher Integration (Cont)

• The integration allows for accurate geometry
  representation, we use CGM tools
• Local mesh control can be done at the edge and
  face levels
• After importing the mesh, we take advantage of
  the mesh visualization tools, preparation of the
  input file for subsequent Finite Element Analyses
  (FE drivers), import of the results and
  post-processing (FE interfaces), available in
  Virtual Lab
• Associativity between mesh and geometry ensure
  easy application of boundary conditions for FE
  analysis

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Main Analysis and Design Flow
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How to build a mesh for something like this?
13 parts 5 assemblies 1 master assembly All parts
are in contact
Need a conforming mesh for modal analysis
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Geometry Extraction

• Top-down assembly organization
• CATProduct documents
• CATPart documents
• Bodies within Part documents
• Domains
• Volumes
• Volumes have a manifold geometry, boundary
  representation. A topology scan is performed to
  extract boundary faces, edges and vertices
• In the end, geometry file is a collection of BRep
  volumes, that can be in contact along faces,
  edges
• Penetrating volumes are not allowed!
• CATIA geometric tolerance 0.001 mm

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Geometry Extraction UV parametrization

• Each face sits on a surface, which has a uv
  parametrization.
• The boundary of each face is represented as a
  collection of uv curves.
• 3D Edges have 3 representations as a segment on
  a 3D curve, and as 2 uv curves in adjacent faces

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Geometry Extraction

• Surface types supported by HMesher are PLANE,
  CANONICAL (Cylinder, Sphere, Torus, Cone) and
  NURBS.
• Not all CATIA surfaces are supported by the
  HMesher.
• The surfaces that have no correspondent are
  converted to the NURBS format, using CATIA
  operators, with a default tolerance of 0.01 mm.

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Basic Flow of HMesher
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Multiple Solid Processing

• Needed for volumes in contact, for conforming
  mesh
• an important advantage for finite element
  analysis, as there are no linkage elements
  needed.
• The solids will share nodes, edges and faces of
  mesh elements

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Multiple Solid Processing

• Intersection is done in UV space of one of the
  faces in contact
• New faces are created with the intersection
  edges, vertices

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Multiple Solid Processing
Face that is common to both solids after multiple
solids processing Non manifold geometry
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Multiple Solid Processing Final mesh
Mesh is compatible along contact face between
solids
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Basic Flow of HMesher
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Facetting Surface Meshing

• Start with breaking the boundary geometry edges
• Performed on each boundary face
• Constrained Delaunay mesh on each face is mapped
  on 3D geometry

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Surface meshing
2d refinement points added in layers
Constrained 2d Delaunay
Scaled uv space
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Surface mesh violations

• Due to curvature and feature proximity, surface
  mesh from different faces can intersect,
  resulting in surface mesh violations

mesh size reductions are performed in those
cases, to eliminate violations
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Basic Flow of HMesher
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Surface Mesh Simplification (Blurring)

• The most effective way of eliminating the small
  edges, thin faces and other small features

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Solid Meshing. Interior Point Generation
Interior points are roughly on the normals from
the closest boundary
Boundary points
Normal direction for layer generation
Points are added in layers from boundary, and are
averaged when fronts collide
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3D Delaunay
Classic 3d Delaunay , we insert all the points of
the surface mesh and interior points in a large
enough tetra
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Trimming / Untrimming

• Conforming Delaunay is performed next add
  trimming points on the faces and edges until
  all faces and edges are part of
  tetrahedralization.
• Remove outside tetrahedrons
• Untrimming Eliminate trimming points if
  possible, maintaining the topology of the model,
  but do not consider anymore Delaunay property

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Trimming / Untrimming
zoom
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Untrimming (Delaunay relaxation)
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Trimming / Untrimming explained in 2D
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Basic Flow of HMesher
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Curve Recovery

• Input Tetrahedralization of the points, and the
  curved representation of the model.
• Output Curved representation of the
  Tetrahedralization
• Algorithm Repeatedly perform the following
• For each edge on the model boundary, map using
  the original curve.
• For each edge on the face interior, map using a
  geodesic curve, maintaining angles with neighbors
• For each edge in the interior, map only if
  necessary to maintain validity
• Interpolate the interior faces.

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Curve Recovery
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Hybrid Meshing
1 Meshkat, S. , Talmor, D. , Generating a
Mixed Mesh of Hexahedra, Pentahedra and
Tetrahedra from an Underlying Tetrahedral Mesh,
International Journal for Numerical Methods in
Engineering. Volume 49, Issue 1-2 , Pages 17
30, July 2000
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Hybrid Meshing

• Uses a subgraph of the topological dual graph
• Tetrahedron vertex in dual graph
• Interior face solid edge in dual graph
• Quadrilateral face on a merged element dotted
  edge in dual graph

Extended RF graph for a pyramid
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Hybrid Meshing
Extended RF graph for a pentahedra (triangular
prism)
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Hybrid Meshing

• Some interesting properties
• RF Graphs for penta or hexa decomposition are
  planar
• The RF-graph of all tetrahedral decompositions
  of a hexahedron into six tetrahedra has exactly
  one cycle.
• The decomposition into five tetrahedra contains
  no cycles
• In a tetrahedral decomposition of a hexahedron, a
  tetrahedron with 3 boundary faces cannot be
  connected to another tetrahedron with 2 or 3
  boundary faces

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Hybrid Meshing
Extended RF graphs for hexahedron there is 1 RF
graph for 5-tetrahedron decomposition
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Hybrid Meshing
Extended RF graphs for hexahedrons 5 different
graphs for 6-tetrahedron decompositions
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Hybrid Meshing
Extended RF graphs for hexahedrons 5 different
graphs for 6-tetrahedron decompositions
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Hybrid Meshing

• Extended RF-graphs are compact way of storing
  conceptual templates for a tetrahedral
  decomposition.
• Since finding hexahedra and pentahedra in a
  tetrahedrization involves finding a subgraph that
  matches a given graph, the use of a graph is
  somewhat inefficient.
• Instead, for a given graph, all possible search
  trees are constructed, one for each root node.
  These six RF-graphs are converted into 14 search
  trees in total
• The algorithm uses actually 31 search trees, for
  hexahedrons that are composed from more than 6
  tetrahedrons (up to 13)

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Hybrid Meshing

• RF graphs are converted to search trees example
  of 2 search trees corresponding to 3-cycle RF
  graph
• The solid lines depict the tetrahedra that
  share a face, whereas dashed lines represent the
  constraint to find a quadrilateral pair.

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Hybrid Meshing

• The RF-graph only establishes graph-theoretical
  conditions for existence of a given polyhedron,
  i.e. hexahedron or pentahedron. Additional
  geometry criteria are necessary to ensure the
  validity of the polyhedron.
• A backtrack algorithm is involved to find
  possible search trees for tetrahedrons in the
  mesh
• A best solution is committed early if found
• The process is expensive (60-80 of total CPU
  time)
• Unless there are at least 2 layers of
  hexas/pentas on the boundary, the mesh cannot be
  used for stress analysis

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Hybrid Meshing

• Quality measures
• Percentage of volume of boundary bricks/wedges
  M1 90
• Percentage of volume of all bricks/wedges
  M3 70
• Percentage of number of boundary bricks/wedges
  M4 55
• Percentage of number of boundary bricks
  M5 30
• Percentage of number of all bricks
  M6 20
• Percentage of number of boundary quads
  M7 60
• For a good stress analysis, all these measures
  should be closer to 100.
• Nevertheless, this meshes can be used
  successfully for modal analysis.

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Zonal Meshing

• In order to mesh large assemblies of relatively
  complex models, like engine blocks, transmission
  cases, a modular approach is introduced we call
  it zonal meshing.
• With zonal approach, design changes are not
  propagated past the contacts between zones
• The contact surfaces are processed first, then
  parts are meshed independently, while preserving
  the surface mesh in the contact area. The most
  difficult problem is to ensure the compatibility
  of meshes between parts, at the contact surfaces,
  effectively constraining the solid mesh to be
  compatible to the mesh at the common surface.
• There are theoretical guarantees of when the
  Delaunay mesh can be constrained (Jonathan
  Shewchuk) Edge protection criteria

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Zonal Meshing
First, create a compatible surface mesh
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Zonal Meshing
The final mesh is compatible between solids
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Zonal Meshing Imprint feature
Imprint feature impose a surface mesh pattern on
a face of the solid
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Engine Block Example
13 parts 5 assemblies 4 zonal interfaces 10000
faces 28000 edges
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Engine Block Example
Define zonal Interfaces
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Engine Block Example
Zonal surface mesh
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Engine Block Example
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Engine Block Hybrid Mesh
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Future Work

• Efficiency needs to be increased
• Merging measures closer to 100
• Memory management
• Robustness and quality will always be issues with
  coarse meshes

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Acknowledgements

• Many thanks to Honda RD Co., Ltd., for
  continuous support and for driving the whole
  process forward.
• Thanks to LMS International for the opportunity
  to work on the HMesher
• Thank you for your attention!